First-Order Logic (FOL), also called predicate logic, is a formal system used in artificial intelligence to represent knowledge and perform logical reasoning about objects and their relationships. It extends propositional logic by introducing predicates, variables, functions, and quantifiers (such as ∀ meaning “for all” and ∃ meaning “there exists”). These elements allow AI systems to describe complex real-world relationships instead of only simple true/false statements.
In FOL, knowledge is expressed using statements about objects in a domain. For example, the statements “All cats are mammals” and “Tom is a cat” can be represented logically, allowing an AI system to infer that “Tom is a mammal.” This ability to derive new knowledge from existing facts makes FOL a powerful tool for knowledge representation, reasoning systems, natural-language processing, and expert systems.
Resolution is a key inference rule used with first-order logic to automatically prove statements or detect contradictions. The resolution method works by converting logical statements into a standardized format called Conjunctive Normal Form (CNF) and then combining clauses that contain complementary literals (for example, P(x) and ¬P(x)). By repeatedly applying this rule, the system generates new clauses until it either finds a contradiction or confirms that the statement can be logically derived.
In artificial intelligence, the combination of FOL and resolution forms the foundation of automated theorem proving and logical reasoning systems. It is widely used in logic programming languages such as Prolog, expert systems, and AI reasoning engines. By structuring knowledge logically and applying systematic inference rules, AI systems can analyze complex problems, derive conclusions, and support intelligent decision-making.
